If $$\frac{x}{y} = \frac{4}{5}{\text{,}}$$   then the value of $$\left( {\frac{4}{7} + \frac{{2y - x}}{{2y + x}}} \right)$$   is?

Solution(By Examveda Team)

$$\eqalign{ & \frac{x}{y} = \frac{4}{5} \cr & \frac{4}{7} + \frac{{2y - x}}{{2y + x}} \cr & = \frac{4}{7} + \frac{{y\left( {2 - \frac{x}{y}} \right)}}{{y\left( {2 + \frac{x}{y}} \right)}} \cr & = \frac{4}{7} + \frac{{\left( {2 - \frac{4}{5}} \right)}}{{\left( {2 + \frac{4}{5}} \right)}} \cr & = \frac{4}{7} + \frac{{10 - 4}}{{10 + 4}} \cr & = \frac{4}{7} + \frac{6}{{14}} \cr & {\text{ = }}\frac{{8 + 6}}{{14}} \cr & {\text{ = }}\frac{{14}}{{14}} \cr & {\text{ = 1}} \cr} $$